different angles same solution

While a student was playing with their calculator they found that sometimes the answers produced from taking the sine and cosine of different angles were the same answer. The information below are some of the examples when this occurs.

sin 55* = 0.819152044 and cos 35* = 0.819152044

sin 30* = 0.5 and cos 60* = 0.5

sin 15* = 0.258819045 and cos 75* = 0.258819045

I have to explain why these calculations produce the same answer.

I looked numerous times at the formula,but i cant come up with anything.